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arXiv · 2003.11322

On the exceptional sets of integral quadratic forms

Wai Kiu Chan·Byeong-Kweon Oh
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Abstract

A collection $\mathcal S$ of equivalence classes of positive definite integral quadratic forms in $n$ variables is called an $n$-exceptional set if there exists a positive definite integral quadratic form which represents all equivalence classes of positive definite integral quadratic forms in $n$ variables except those in $\mathcal S$. We show that, among other results, for any given positive integers $m$ and $n$, there is always an $n$-exceptional set of size $m$ and there are only finitely many of them.

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Wai Kiu Chan, Byeong-Kweon Oh. 2020-03-25. On the exceptional sets of integral quadratic forms. https://arxiv.org/abs/2003.11322

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